The combine wave-current flow has been solved by researchers by assuming wave over either depth-wise constant or linearly current profile. Some complicated non-linear current profiles have also been considered to simulate various shear currents. In this paper, a non-linear current, vertically logarithmic in nature is considered and its interaction with a periodic surface wave is examined. Navier - Stokes equations for incompressible flow are solved for the current part and by using periodic boundary conditions; effect of logarithmic current on wave components is assessed. The corresponding celerity and dispersion equation yields a close form solution for the shallow wave approximation. Several comparative trends between wave-only, wave with log current and with constant current for the wave following/opposing these currents have been discussed. The flow properties of the first order are presented which can be applicable to the real inland and coastal flows where progressive waves are ubiquitous over depth-wise logarithmic current. The work is further extended to the second order semi-empirical wave component using past experimental data on wave spectrum of combine flow.

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